IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting
A bank in Pune quotes a nominal annual interest rate of 12% convertible monthly on a deposit. What is the effective annual rate, to two decimal places?
The effective annual rate is 12.68%. A nominal 12% convertible monthly gives 1% per month, and compounding for twelve months gives 1.01 to the power 12, which is 1.126825, so the effective rate is 12.68%.
- A12.00%
- B12.36%
- C12.68%Correct
- D12.55%
- 13.20%
Explanation
Monthly rate = 1%. Effective annual rate = 1.01^12 - 1 = 1.126825 - 1 = 12.68%. Option 12.36% comes from using quarterly compounding (1.03^4 - 1), and 12.00% ignores compounding.
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